CANTON - Count on Cantor

no tags 

One of the famous proofs of modern mathematics is Georg Cantor's demonstration that the set of rational numbers is enumerable. The proof works by using an explicit enumeration of rational numbers as shown in the diagram below.

1/1 1/2 1/3 1/4 1/5 ...
2/1 2/2 2/3 2/4
3/1 3/2 3/3
4/1 4/2
5/1

In the above diagram, the first term is 1/1, the second term is 1/2, the third term is 2/1, the fourth term is 3/1, the fifth term is 2/2, and so on.

Input

The input starts with a line containing a single integer t <= 20, the number of test cases. t test cases follow.

Then, it contains a single number per line.

Output

You are to write a program that will read a list of numbers in the range from 1 to 10^7 and will print for each number the corresponding term in Cantor's enumeration as given below.

Example

Input:
3
3
14
7

Output:
TERM 3 IS 2/1
TERM 14 IS 2/4
TERM 7 IS 1/4

hide comments
bhushangawde: 2016-05-16 08:10:43

easy AC in one go! :D My 20th !!

satoruu: 2016-04-23 00:21:21

Once you get the pattern, it will be easy. Think about math and geometry.

P.S: It was kinda funny, got WA on my first try because I was writing "is" instead of "IS", so watch out :)

gautam: 2016-04-03 11:44:44

yooo!!..ac

ydeepak1889: 2016-02-23 17:00:38

AC in go .....My 22 nd .... :)

arpitkath: 2016-02-14 14:58:20

After 2 hours work and filling 3 pages..AC..:)..superb concept

boovi: 2016-01-22 07:31:15

easy one:)

try2catch: 2016-01-17 11:47:52

My 1st to be AC in 1st go :) easy though!
try this - Given a/b , find its position without using loop or recursion.

abc_c: 2016-01-06 15:43:29

My 22nd...AC in 1 go :)

rocode0001: 2015-12-04 12:03:59

Awesome!!!

aloochaat1998: 2015-11-28 03:35:22

observe the pattern very carefully and use the formula for sum of n numbers.AC in 1 go! :)


Added by:Thanh-Vy Hua
Date:2005-02-27
Time limit:5s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS PERL 6 VB.net
Resource: ACM South Eastern European Region 2004